How to make a page template to list all galleries?

The underlying question here is How do I query all posts with image galleries? (since, once you have such a query, creating a custom template page to loop through them is fairly trivial).

One method would be:

1. Custom query of attachment posts with a mime_type of image
2. Loop through them, and add $post->post_parent to an array
3. Custom query of posts, passing the above array of post IDs as post__in
4. Loop through them, and output whatever you would like for each

Perhaps like so:

<?php
// Custom query args for image attachments
$image_attachments_query_args = array(
    'post_type' => 'attachment',
    'mime_type' => 'image'
);
// Query image attachments
$image_attachments = new WP_Query( $image_attachments_query_args );

// Loop through them and get parent post IDs
$gallery_post_ids = array();

foreach ( $image_attachments as $image_attachment ) {
    $gallery_post_ids[] = $image_attachment->post_parent;
}

// Custom query args for gallery posts
$gallery_posts_query_args = array(
    'post__in' => $gallery_post_ids
);

// Query gallery posts
$gallery_posts = new WP_Query( $gallery_posts_query_args );

// Loop through gallery posts

if ( $gallery_posts->have_posts() ) : while ( $gallery_posts->have_posts() ) : $gallery_posts->the_post();
    // Loop output goes here
endwhile; endif;
wp_reset_postdata();
?>

Note that this pulls all posts with even a single image attachment. You could maybe get fancy when looping through image attachments, and do something like:

// Placeholder array for IDs
$temp_post_ids();

// Final array for gallery post IDs
$gallery_post_ids = array();

// Loop through them and get parent post IDs
foreach ( $image_attachments as $image_attachment ) {
    // Add ID to the placeholder array
    $temp_post_ids[] = $image_attachment->post_parent;
    // If this post ID has multiple image attachments,
    // add it to the gallery posts query;
    // This will prevent posts with only a single
    // attached image from being queried in the next step
    if ( in_array( $image_attachment->post_parent, $temp_post_ids ) ) {
        $gallery_post_ids[] = $image_attachment->post_parent;
    }
}